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A circle with center (1, 0) and radius 2 lies in the coordinate plane

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A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 09 Sep 2018, 08:51
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Difficulty:

  45% (medium)

Question Stats:

57% (01:42) correct 43% (01:11) wrong based on 21 sessions

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A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle, is (x, y) in quadrant II?

(1) |y| < 1
(2) |x| < 1

Attachment:
image001.jpg
image001.jpg [ 1.42 KiB | Viewed 235 times ]

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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane  [#permalink]

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New post 09 Sep 2018, 10:02
Top Contributor
Bunuel wrote:
Image
A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle, is (x, y) in quadrant II?

(1) |y| < 1
(2) |x| < 1

Attachment:
image001.jpg


Target question: Is (x, y) in quadrant II?

Given: A circle with center (1, 0) and radius 2 lies in the coordinate plane
Let's sketch the circle along with some key points on the circle:
Image

From here, let's jump to . . . .

Statements 1 and 2 combined
There are several points on the circles that satisfy BOTH statements. Here are two cases:

Case a: The point lies slightly above and to the right of (-1,0).
Image
Notice that the x-coordinate is between -1 and 0, so we can be certain that |x| < 1
Likewise, the y-coordinate is slightly greater than 0, which means |y| < 1
In this case, the answer to the target question is YES, the point (x,y) IS in quadrant II

Case b: The point lies slightly below and to the right of (-1,0).
Image
Notice that the x-coordinate is between -1 and 0, so we can be certain that |x| < 1
Likewise, the y-coordinate is slightly less than 0, which means |y| < 1
In this case, the answer to the target question is NO, the point (x,y) is NOT in quadrant II

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Re: A circle with center (1, 0) and radius 2 lies in the coordinate plane &nbs [#permalink] 09 Sep 2018, 10:02
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